Advertisements
Advertisements
प्रश्न
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
Advertisements
उत्तर
In the given problem, we have to find the value of `x^3 + 1/x^3.`
Given: `x^4 + 1/x^4 = 194`
We know that,
`(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
Now, substituting the given value
`(x^2 + 1/x^2)^2 = 194 + 2`
∴ `(x^2 + 1/x^2)^2 = 196`
∴ `x^2 + 1/x^2 = sqrt196`
∴ `x^2 + 1/x^2 = +-14`
Let’s relate it to `x^3 + 1/x^3`
`(x + 1/x)^2 = x^2 + 1/x^2 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
`(x + 1/x)^2 = 14 + 2`
∴ `x + 1/x = sqrt16`
∴ `x + 1/x = +-sqrt4`
Thus,
`x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x)`
`x^3 + 1/x^3 = (4)^3 - 3(4)`
`x^3 + 1/x^3 = 64 - 12`
∴ `x^3 + 1/x^3 = +-52`
संबंधित प्रश्न
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
If a + b = 10 and ab = 21, find the value of a3 + b3
Find the following product:
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
If a − b = −8 and ab = −12, then a3 − b3 =
Find the square of `(3a)/(2b) - (2b)/(3a)`.
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
If p + q = 8 and p - q = 4, find:
p2 + q2
If m - n = 0.9 and mn = 0.36, find:
m + n
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
The coefficient of x in the expansion of (x + 3)3 is ______.
Using suitable identity, evaluate the following:
101 × 102
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
